This is the commonly used English
phrase (even among Muslims), but the
Arabic phrase is actually (salla-Allahu alaihi wa sallam), which is more correctly translated as "May the praises of Allah and peace be upon him".
However, since Muslims believe in other prophets such as Moses and Jesus (only they believe that they were human and had the same basic message as Islam -- the unity of God), they also bestow the honorific "peace be upon him" (in Arabic: alayhi-al-salaam) upon other prophets.
Also, for the followers and companions of Prophet Muhammad, Muslims frequently use the phrase "radi-Allahu-anh" which means: "May God be pleased with him/her".